de Prisco, Renato

Eshraqi, Mohammad

Karlsson, Anders

Miyamoto, Ryoichi

Sargsyan, Edgar

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00Error study on the normal conducting ESS linacde Prisco, Renato; Karlsson, Anders; Eshraqi, Mohammad; Miyamoto, Ryoichi; Sargsyan,Edgar2014Link to publicationCitation for published version (APA):de Prisco, R., Karlsson, A., Eshraqi, M., Miyamoto, R., & Sargsyan, E. (2014). Error study on the normalconducting ESS linac. 942-944. Paper presented at LINAC2014.Total number of authors:5General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.ERROR STUDY ON THE NORMAL CONDUCTING ESS LINACR. De Prisco∗, ESS, Lund, Sweden and Lund University, Lund, SwedenM. Eshraqi, R. Miyamoto, E. Sargsyan, ESS, Lund, SwedenA. Karlsson, Lund University, Lund, SwedenAbstractOne of the preliminary, but important test to evaluatethe robustness of the accelerator design is performing thestatistical error study by introducing realistic tolerances onthe machine components.In this paper the guidelines to define the tolerances andthe correction system are summarized in order to validatethe design. Firstly statistical studies have been performedin order to define the sensitivity to single errors and to fixthe tolerances. Then all errors, within the previous definedtolerances, are applied with the correction system to evaluatethe beam quality and to check if the system guarantees aradiologically safe operation.INTRODUCTIONThe European Spallation Source (ESS) uses a LINear AC-celerator (LINAC) to deliver the high intensity proton beamto the target station. The normal conducting ESS LINACaccelerates a proton beam of 62.5mA from 0.075MeV to89.68MeV at 352.21MHz. The pulses are 2.86ms longwith a duty cycles of 4%. Permanent Magnet Quadrupoles(PMQs) in the DTL are used as focusing elements in a FODOlattice. The average beam power is 5MW with a peak beampower at target of 125MW.SPACE CHARGE ROUTINEThe first crucial point to accurately describe the spacecharge effect of the high current LINAC is to choose a properspace charge routine. For these studies the PICNIC routineis chosen because, by applying the errors, the assumption ofcylindrical symmetry on the bunch shape can not be guaran-teed [1].The second crucial point is the choice of the mesh sizein the beam and the particle number. There is an optimummesh size respect to which a larger mesh size deteriorates theresolution whereas a smaller mesh size induces a small num-ber of particle per cell and, consequently, statistical noise.For these studies the mesh size is 15 both in transverse andin longitudinal planes. The number of particles is 1million.ERROR STUDY STRATEGYThe normal conducting ESS LINAC is composed of threestructures: Radio Frequency Quadrupole (RFQ), MediumEnergy Beam Transport (MEBT), Drift Tube Linac (DTL).For each section, at first, each error is applied individuallyto evaluate the emittance growth sensitivity. At this stage theerrors are analyzed without the correction steerers. In a very∗ renato.deprisco@esss.sepreliminary approach the additional emittance growths, dueto the individual errors, in the k−plane, ∆εk (with respectto the emittance growths in the case without error in thesame plane, εout, NO ERR, k ) can be considered as independentvariables. With this hypothesis a rough value of the totalsquared additional emittance growth, for the case in whichall errors are applied simultaneously, can be approximatedby the sum of the squared individual additional growths.This calculation is useful to fix a preliminary acceptablelimit for each error.The additional emittance growth is defined as:∆εk =εout, ERR, k − εout, NO ERR, kεout, NO ERR, k, (1)where εout, ERR, k is the output emittance in presence of errorsin the k−plane.In the second step all the errors are applied simultaneouslywith the corrector steerers. A fine tuning on the tolerances isdone in order to have the total additional emittance growthlimited to 10% per structure and the losses less than 1W/meverywhere. Finally a steerer study is done for the DTLby varying their number, position and strength in order toreduce further the losses.Each case is simulated using 1000 linacs.ERROR DEFINITIONSIt is possible to separate the errors in two categories:static and dynamic in time. To the static category belong:quadrupole transverse position, dx, dy, rotation, dφx , dφy ,dφz , and gradient, dG, errors; structure to structure align-ment, dxT , dyT , errors; field amplitude, dE0, and phase,dφs , error; klystron field, dEk , and phase, dφk , error. Theklystron field, dEk,d , and the phase, dφk,d , jitter error belongto the dynamic category.RFQ AND MEBTThe beam is generated at the RFQ input with a gaussiandistribution truncated at 4σ. The nominal RFQ output dis-tribution is saved and used in the MEBT and global errorstudies. The main beam parameters at the RFQ output andthe tolerances for the RFQ and MEBT are reported in [2].The effective gap voltage of the three bunchers in the MEBTare tuned to match the Twiss input DTL parameters. TheMEBT output Twiss parameters and, in parentheses, theirdifference, in percentage, from the input ideal Twiss Param-eters of the DTL are reported in Table 1.By introducing in the MEBT the tolerances defined in [2]it is possible to define the variation interval for each outputbeam parameter. The intervals are reported in the Table 2.THPP042 Proceedings of LINAC2014, Geneva, SwitzerlandISBN 978-3-95450-142-7942Copyright©2014CC-BY-3.0andbytherespectiveauthors02 Proton and Ion Accelerators and Applications2A Proton Linac ProjectsTable 1: Nominal Twiss Parameters at the MEBT Outputα β ε[mm/π.mrad] [mm.π.mrad]X 1.34 (-6.4%) 0.21 (-3.3%) 0.28Y -4.18 (-2.2%) 0.76 (-3.7%) 0.29Z 0.13 (-0.8%) 0.41 (-0.5%) 0.37Table 2: Beam Parameter Intervals at the MEBT OutputParameter Unit Intervalx [mm] −0.002 ± 0.204y [mm] 0.003 ± 0.421x ′ [mrad] −0.012 ± 1.168y′ [mrad] 0.025 ± 2.065dE [keV] −0.759 ± 7.613αx 1.338 ± 0.118βx [mm/mrad] 0.215 ± 0.016αy −4.189 ± 0.308βy [mm/mrad] 0.764 ± 0.040αz −0.120 ± 0.062βz[deg/MeV]273.7 ± 20.5The histogram of the occurrences of each parameter atthe MEBT output has a gaussian shape. The width of eachinterval in the Table 2 is equal to 0.5 ×√2 π × σ and it isalso half base length of a rectangle with height equal to themaximum of the gaussian (σ is the standard deviation of theapproximant gaussian function).DTLThe actual DTL design [3] consists of 5 tanks with anideal constant accelerating field integral in each tank. Evenif the cells, different in length, have the same frequency, theaccelerating field integral is not the same for all the cells ofeach tank. This is due to the fact that there is not a perfectmode matching between the adjacent cells built individually.The mismatch produces a natural tilt of the accelerating fieldintegral along the cells that must be compensated.The Accelerating Field Tuning ErrorWe define nominal accelerating field integral, E0, thefield after the compensation [4] and accelerating field tuningerror its difference with respect to the ideal constant one.The nominal E0 is, on average, within 0.18% of its idealvalue [3]. In all of the following error studies we considerthat the accelerating field in the DTL is the nominal one thatcan be affected by other errors (dE0, dEk , dEk,d).The Natural Emittance GrowthWe investigate the sensitivity to each individual in twocases: by using a gaussian distribution, cut at 3σ, matchedat the DTL input and by using the MEBT output distribu-tion. We define natural emittance growth as the emittancegrowth in the DTL when this structure is affected only bythe accelerating field tuning error. The natural emittancedue to a gaussian matched (at the DTL input) distribution,∆εnat, G , and due to a MEBT output distribution, ∆εnat, M ,are reported in Table 3. For the Gaussian case we use asinput emittance, both in X and Y, an average between thetwo homologous values at the MEBT output.Table 3: Natural Emittance Growthε in, G , ε in, M εout, G , εout, M ∆εnat, G, M[mm.π.mrad] [mm.π.mrad] [%]X 0.2857, 0.2832 0.3034, 0.2947 6.2, 4.1Y 0.2857, 0.2882 0.3020, 0.2976 5.7, 3.3Z 0.3728, 0.3728 0.3872, 0.3840 3.9, 3.0Table 3 shows that the natural emittance growth is higherwhen a gaussian distribution, matched to the DTL input, isused.Individual ErrorsThe more relevant additional emittance growths, due tothe individual errors, are shown in the Fig. 2, but the samestudy is done for all the errors mentioned before. It is im-portant to underline that the error on the accelerating field isnot studied by varying randomly the field cell by cell in eachtank: such an approach does not agree with the Maxwellequations. For each run, random, but limited, volume per-turbations are applied, cell by cell, so that the acceleratingfield, calculated tank by tank, is within a desired percentagefrom its nominal value. From these studies it is evident thatthe MEBT distribution induces higher additional emittancegrowth.Multipole StudiesIn Fig. 1 we report only the additional transverse emit-tance growth due to the individual higher-order (n=3, 4, 5)multipole components since the longitudinal one is not rele-vant. Their magnitudes are expressed in percentage of thequadrupole strength at 3/4 of bore radius from the beam axis.∆ε is negligible for quadrupole and dodecapole. For all theruns there are no losses.0.2 0.4 0.6 0.8 100.20.4Gn [%]∆ε[%]∆ε x, 3 ∆εy, 3∆ε x, 4 ∆εy, 4∆ε x, 5 ∆εy, 5Figure 1: Additional emittance growth due to the multipoles.An error study is done by introducing all the higher-ordermultipole with a maximum gradient of 1%. The transverseadditional emittance growth is 0.5%. The effect can beamplified in presence of other errors because the centroidoscillation and the growth of the beam dimension induceProceedings of LINAC2014, Geneva, Switzerland THPP04202 Proton and Ion Accelerators and Applications2A Proton Linac ProjectsISBN 978-3-95450-142-7943 Copyright©2014CC-BY-3.0andbytherespectiveauthorsmore particles where the multipole field is more strong. Anerror study is running to evaluate this effect.6 · 10−2 8 · 10−2 0.1 0.12 0.14024dx [mm]∆ε[%]∆ε x, G ∆εy, G ∆ε z, G∆ε x, M ∆εy, M ∆ε z, M0.1 0.15 0.2 0.25024dφz[deg]∆ε[%] ∆ε x, G ∆εy, G ∆ε z, G∆ε x, M ∆εy, M ∆ε z, M0.3 0.4 0.5 0.6 0.700.511.52dG [%]∆ε[%] ∆ε x, G ∆εy, G ∆ε z, G∆ε x, M ∆εy, M ∆ε z, M0.6 0.8 1 1.2 1.400.511.5dE0 [%]∆ε[%] ∆ε x, G ∆εy, G ∆ε z, G∆ε x, M ∆εy, M ∆ε z, M0.6 0.8 1 1.2 1.400.20.40.60.81dφs[deg]∆ε[%] ∆ε x, G ∆εy, G ∆ε z, G∆ε x, M ∆εy, M ∆ε z, MFigure 2: ∆ε due to the individual errors.TolerancesOne possible set of tolerances that keeps the losses below1W/m, when the beam is transported through all the previoussections with their tolerances, is reported in Table 4.Steerer StudiesTo reduce the losses, two additional steerers, X and Y,are placed in the MEBT with an additional beam positionmonitor in the first DTL drift tube. Table 5 shows the totalpower loss as function of the maximum steerer strength, SMand the percentage of the cases that has a power loss less thanTable 4: DTL Tolerances.Parameter Tolerancedx, dy [mm] 0.1dφx , dφy , dφz [deg] 0.5, 0.5, 0.2∆G [%] 0.5∆E0,∆Ek ,∆Ek,d [%] 1, 1, 0.2∆φs ,∆φk ,∆φk,d [deg] 0.5, 1, 0.2dxT , dyT [mm] 0.1the reported value. It is clear that, having fixed the steererposition, there is an optimum SM for which the losses areminimized. An increase of SM can cause of higher losses.Table 5: Total Loss as Function of Steerer StrengthSM Total Loss90% 99% 100%[G.m] [W] [W] [W]4 0.52 1.95 9.948 0.47 1.95 6.7512 0.59 2.92 14.2616 0.87 4.55 21.32CONCLUSIONThe error study shows that the normal conducting sectionof the ESS LINAC is robust: the total ∆ε is around 6% forboth MEBT and DTL and, as shown in the Fig. 3, the lossesof 99% of the cases are less than 1W/m if SM=8G.m.0 10 20 30 4000.20.40.60.81z [m]Losses[W]Figure 3: Losses in MEBT and DTL.REFERENCES[1] N. Pichoff et al., “Simulation Results with an Alternate 3DSpace Charge Routine, PICNIC,” LINAC’98, August 1998,MO4042, p. 141[2] M. Eshraqi et al., “Statistical Error Studies in the ESS Linac,”IPAC’14, Dresden, June 2014, THPME044, p. 3323[3] R. De Prisco et al., “ESS DTL Status: Redesign and Optimiza-tions,” IPAC’14, Dresden, June 2014, THPME041, p. 3314[4] R. De Prisco et al., “ESS DTL RF MODELIZATION: FIELDTUNING AND STABILIZATION,” IPAC’13, Shanghai, May2013, THPWO070, p. 3918THPP042 Proceedings of LINAC2014, Geneva, SwitzerlandISBN 978-3-95450-142-7944Copyright©2014CC-BY-3.0andbytherespectiveauthors02 Proton and Ion Accelerators and Applications2A Proton Linac Projects

Error study on the normal conducting ESS linac

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